One Token Against Two

At an arcade, Rui challenges Sana to a series of one-token games: each round the loser hands one token to the winner, and Rui wins any given round with probability $\frac{2}{3}$, independently of the rest. Rui starts with 1 token and Sana with 2, and they keep playing until one of them holds all 3 tokens. What is the probability that Rui wins everything?